南水北调中线总干渠河南段非恒定流数值模拟研究
|
摘要
南水北调中线工程是为解决我国水资源分布不均并严重影响北方地区经济发展问题而兴建的一项特大型跨流域，具有战略性意义的宏伟工程。明渠输水是开敞式输水系统，它的特点是具有较大的超设计输水能力；而由于地形或其它建筑物交叉等原因，在调水工程中的长距离输水系统中，需要采用明渠和有压管道相结合的形式；明渠中的非恒定流往往是由闸门或泵站的开启和关闭等人为因素导致；为满足实际输水的需要，需要进行水力过渡过程计算，确定由各种原因引起系统非恒定流时该系中的水位、流量、流速、水深等水力要素沿流程和随时间的变化规律，以设计出更加优化的长距离输水系统，因此水力过渡过程是长距离输水系统中普遍存在的现象。进行非恒定流数值模拟计算，分析过渡过程中的水流特性，对输水系统的设备的设计和运行都具有重要意义。
本论文主要以明渠非恒定流理论为基础，从南水北调中线工程总干渠河南段的具体工程情况出发，针对长距离输水系统中存在多处渡槽、暗渠、倒虹吸及连接段等复杂连接管道的明渠非恒定流数值模拟方法展开研究，并对惯性水头及糙率选取的影响进行深入的分析，最后通过对非常运用工况最高水位推算及控制关闸方式的改变，分析水面线的变化，定性分析最佳调度方式，以便对实际工程中调度运行方式进行指导，同时为了更好的服务于实际工程，对数值模拟的可视化进行研究，具体将围绕以下几个方面展开：
1．首先建立对简单棱柱形渠道在设计流量下启闭闸门时的非恒定流数学模型，并采用多种计算方法进行数值模拟，对计算结果进行比较，选用最佳计算方法。
2．对节制闸突然关闭使渠道中流速突然变化所引起的水位交替升降的水力现象进行全面理论分析。
3．从一维明渠及有压管非恒定流连续性方程和运动方程出发，详细论述管渠结合中各类边界条件的处理方法；并结合南水北调中线工程某段实例，对运行中上下游闸门同时关闭工况下下游闸前水深的变化情况进行模拟。
4．从能量角度出发，分析管渠结合一维非恒定流系统中倒虹吸进出口断面能量损失，对是否考虑有压管惯性水头的影响进行分析比较，并分析糙率的选取对水面线的敏感度。
5．通过控制关闸方式改变边界条件，分析水面线的变化，定性分析最佳调度方式，以便对实际工程中调度运行方式进行合理指导。
6．论文利用Matlab语言编制程序计算，用VisualBasic开发应用程序，对南水北调中线总干渠河南段所有节制闸在非常运行工况下的数值模拟结果进行可视化显示。最后显示以下四类渠段运行结果图：
a)断面流量随时间变化图
b)断面水深随时间变化图
c)某一时刻各断面流量变化图
d)某一时刻各断面水深变化图
The Middle Route of South-to-North Water Transfer Project is a great strategic significance water transfer project which has been programmed and built in China across drainage basin in order to solve the water resources problem in northern areas. Channel flow is a opening wide -like water transfer system with the bigger ultra design water head. As the reasons of terrain or other buildings overlapping and so on, the Canal-pipes conjunctive system is needed in the long distance water transfer project. Unsteady channel flow has always been caused by the opening or closure of strobe and pumping station. In order to satisfy the water distribution, it is necessary to simulate on the water power transient processing and to determine the rules which follows the change of flow and time of every hydraulic elements as water level, current capacity, speed of flow, water depth in unsteady channel flow system which is caused by all kinds of reasons, and then to design the optimizes items in the long distance water - carriage system. Therefore the water power transient process is the common phenomenon in the long distance water - carriage system. It has vital significance to design and operate the water-carriage system's equipment to simulate the unsteady flow and to analysis the fluent characteristic of the transient process.
This paper mainly takes the unsteady flow theory as a foundation, it bases on the concrete situation of the main channel in the South -North Water Transfer to the Middle Route Project (He Nan section), it studies on unsteady flow simulation method of all kinds of complex conjunctions in the long distance water - carriage system, such as aqueducts、covered ditches、inverted siphons、connection sections and so on . and it deeply analyzes the impacts on choosing the inertia head and the roughness.Finally ,it analyzes the changes of water surfaced and the optimal dispatching control by calculating the highest water level and changes the control pattern of closing the gate under special working condition, so that it can afford effective theory guidance in the actual project. At the same time ,in order to provide better service for the actual project, it has researched on visualization in unsteady flow numerical simulation . Its main ideas are shown as follows:
1. Firstly establishing numerical models for unsteady flow in simple prismatic channel under the design discharge when the gate lifting, introducing some calculation methods to calculate, and comparing the results ,and then selecting the best method of calculation.
2. Secondly, completely discussing the theoretical analysis of water power phenomena of rise and fall of water level which is caused by sudden closing of the control sluice lead to the sudden flow rate change.
3. Thirdly, based on the continuity equation and dynamic equation of one-dimensional open channel and confined tunnel, detailing different processing methods of boundary conditions researches in the canal-pipes conjunctive system. Then taking a project in the South -North Water Transfer to the Middle Route as a example simulating the water depth before the downstream gate when the upstream and downstream gate in generation are shut at the same time
4. Fourthly, analyzing the energy loss of cross-section of Series connection inverted siphons of canal systems based on the energy theorem principle. Paying attention to and comparing the inertia force in this procedure through calculating, and analyzing the water facial suture sensitivity of roughness coefficient selection.
5. Fifthly, changing the boundary condition, analyzing the changes of water surface and selecting the optimal dispatching control by changing the control pattern of closing gates, so that it can afford effective theory guidance in the actual project.
6. In this paper, Matlab language is used on numerical computation, and Visual Basic language is used to establish an application program. It demonstrates the visualization of numerical simulation results of all gates control pattern under special working condition in He Nan Canal Section in Middle Line of S-N Water Transfer Project.
Finally, four kinds of charts on results about canal sections are shown as follows:
a) charts about the variation of Discharge of Cross Section with time .
b) charts about the variation of water depth with time.
c) charts about the variation of Discharge of Cross Section at one moment.
d) charts about the variation of water depth at one moment.
本论文主要以明渠非恒定流理论为基础，从南水北调中线工程总干渠河南段的具体工程情况出发，针对长距离输水系统中存在多处渡槽、暗渠、倒虹吸及连接段等复杂连接管道的明渠非恒定流数值模拟方法展开研究，并对惯性水头及糙率选取的影响进行深入的分析，最后通过对非常运用工况最高水位推算及控制关闸方式的改变，分析水面线的变化，定性分析最佳调度方式，以便对实际工程中调度运行方式进行指导，同时为了更好的服务于实际工程，对数值模拟的可视化进行研究，具体将围绕以下几个方面展开：
1．首先建立对简单棱柱形渠道在设计流量下启闭闸门时的非恒定流数学模型，并采用多种计算方法进行数值模拟，对计算结果进行比较，选用最佳计算方法。
2．对节制闸突然关闭使渠道中流速突然变化所引起的水位交替升降的水力现象进行全面理论分析。
3．从一维明渠及有压管非恒定流连续性方程和运动方程出发，详细论述管渠结合中各类边界条件的处理方法；并结合南水北调中线工程某段实例，对运行中上下游闸门同时关闭工况下下游闸前水深的变化情况进行模拟。
4．从能量角度出发，分析管渠结合一维非恒定流系统中倒虹吸进出口断面能量损失，对是否考虑有压管惯性水头的影响进行分析比较，并分析糙率的选取对水面线的敏感度。
5．通过控制关闸方式改变边界条件，分析水面线的变化，定性分析最佳调度方式，以便对实际工程中调度运行方式进行合理指导。
6．论文利用Matlab语言编制程序计算，用VisualBasic开发应用程序，对南水北调中线总干渠河南段所有节制闸在非常运行工况下的数值模拟结果进行可视化显示。最后显示以下四类渠段运行结果图：
a)断面流量随时间变化图
b)断面水深随时间变化图
c)某一时刻各断面流量变化图
d)某一时刻各断面水深变化图
The Middle Route of South-to-North Water Transfer Project is a great strategic significance water transfer project which has been programmed and built in China across drainage basin in order to solve the water resources problem in northern areas. Channel flow is a opening wide -like water transfer system with the bigger ultra design water head. As the reasons of terrain or other buildings overlapping and so on, the Canal-pipes conjunctive system is needed in the long distance water transfer project. Unsteady channel flow has always been caused by the opening or closure of strobe and pumping station. In order to satisfy the water distribution, it is necessary to simulate on the water power transient processing and to determine the rules which follows the change of flow and time of every hydraulic elements as water level, current capacity, speed of flow, water depth in unsteady channel flow system which is caused by all kinds of reasons, and then to design the optimizes items in the long distance water - carriage system. Therefore the water power transient process is the common phenomenon in the long distance water - carriage system. It has vital significance to design and operate the water-carriage system's equipment to simulate the unsteady flow and to analysis the fluent characteristic of the transient process.
This paper mainly takes the unsteady flow theory as a foundation, it bases on the concrete situation of the main channel in the South -North Water Transfer to the Middle Route Project (He Nan section), it studies on unsteady flow simulation method of all kinds of complex conjunctions in the long distance water - carriage system, such as aqueducts、covered ditches、inverted siphons、connection sections and so on . and it deeply analyzes the impacts on choosing the inertia head and the roughness.Finally ,it analyzes the changes of water surfaced and the optimal dispatching control by calculating the highest water level and changes the control pattern of closing the gate under special working condition, so that it can afford effective theory guidance in the actual project. At the same time ,in order to provide better service for the actual project, it has researched on visualization in unsteady flow numerical simulation . Its main ideas are shown as follows:
1. Firstly establishing numerical models for unsteady flow in simple prismatic channel under the design discharge when the gate lifting, introducing some calculation methods to calculate, and comparing the results ,and then selecting the best method of calculation.
2. Secondly, completely discussing the theoretical analysis of water power phenomena of rise and fall of water level which is caused by sudden closing of the control sluice lead to the sudden flow rate change.
3. Thirdly, based on the continuity equation and dynamic equation of one-dimensional open channel and confined tunnel, detailing different processing methods of boundary conditions researches in the canal-pipes conjunctive system. Then taking a project in the South -North Water Transfer to the Middle Route as a example simulating the water depth before the downstream gate when the upstream and downstream gate in generation are shut at the same time
4. Fourthly, analyzing the energy loss of cross-section of Series connection inverted siphons of canal systems based on the energy theorem principle. Paying attention to and comparing the inertia force in this procedure through calculating, and analyzing the water facial suture sensitivity of roughness coefficient selection.
5. Fifthly, changing the boundary condition, analyzing the changes of water surface and selecting the optimal dispatching control by changing the control pattern of closing gates, so that it can afford effective theory guidance in the actual project.
6. In this paper, Matlab language is used on numerical computation, and Visual Basic language is used to establish an application program. It demonstrates the visualization of numerical simulation results of all gates control pattern under special working condition in He Nan Canal Section in Middle Line of S-N Water Transfer Project.
Finally, four kinds of charts on results about canal sections are shown as follows:
a) charts about the variation of Discharge of Cross Section with time .
b) charts about the variation of water depth with time.
c) charts about the variation of Discharge of Cross Section at one moment.
d) charts about the variation of water depth at one moment.
引文
[1] 魏昌林等，中国南水北调，中国农业出版社2000．10
[2] 张修真等，南水北调—中国可持续发展的支撑工程，中国水利水电出版社．1999．6
[3] 黄伟雄，徐颂，我国南水北调方案的对比与优化设想，佛山科学技术学院学报，2001，19(4)，50～56
[4] 梁海涛．南水北调中线工程河南段总干渠设计．防渗技术．1999．Vol．5N0．2．34-35
[5] 阎占元等，中线南水北调概况与区域发展研究，地域研究与开发1995．12
[6] 水利部长江水利委员会长江勘测规划设计院，南水北调中线工程规划(2001年修订)专题报告．2001．7
[7] 张志明，陈烈奔，张颖君．南水北调中线工程总干渠水面线研究[J]．人民长江2006 Vol．37，No．2
[8] 杨立信等编译，国外调水工程，北京：中国水利水电出版社，2003．
[9] 宋祖诏，张思俊，詹美礼，取水工程，北京：中国水利水电出版社，2002，1-3．
[10] 徐元明，国外跨流域调水工程建设与管理综述，人民长江，1997，28(3)，11-13．
[11] 沈佩君，邵东国，郭元裕，国内外跨流域调水工程建设的现状与前景，武汉水利电力大学学报，1995，28(5)，463～469
[12] 沈洪，国外调水工程纵横谈，四川水利，2000，21(5)，56～58
[13] Costantino,M.L.;Fiore, G.B.;Guadagni,G.;;Fumero,R;Montevecchi,F.M.Fluiddynamic optimization of the pumping oxygenator: CFD simulation and in vitro test. ASAIO Journal, vol 46,no.2, Mar-Apr, 2000
[14] Craig, K.;DeTraversay, C.:Bowen,B.;Essemiani,K.;Levecq,C.;Naylor, R.Hydra u-lic study and optimization of water treatment processes using numerical simulation. Water Science and Technology: Water Supply, Vol 2,No. 5-6,2002
[15] Yang,James (Vattenfall Utveckling AB ) ;Hemstrom,Bengt.CFD-a useful tool in spillway capacity determination.International Conference on Hydraulic Engineering Software, Hydrosoft,Proceedings,1998
[16] Chilton,Richard(Bechte Water Technology Ltd);Stainsby, Richard;Thompson, Susan.Design of the sewage sludge pumping systems. Journal of Hydraulic Research/De Recherches Hydrauliques, Vol 34,No.3, 1996
[17] 黄东，郑国栋，郑邦民．明渠非恒定流数值模拟[J]．工程设计CAD与智能建筑．1999(10)
[18] 林秉南，明渠不恒定流研究的现状和发展，林秉南论文选集，中国水利 水电出版社，2000，340～373
[19] 钱木金，蔡云美．解明渠非恒定流的混合网格法[J]．人民长江，1996
[20] 邓家泉．二维明渠非恒定水流BGK数值模拟[J]．水利学报，2002(4)
[21] 邓家泉．以玻尔兹曼方程建立明渠水流模型的理论基础[J]．人民珠江，2000(6)
[22] 余国安．闸门调控下的灌溉渠道非恒定流数值模拟研究．西北农林科技大学硕士学位论文，2004
[23] 美国内务部垦务局编著．庞进武、高占义等译．渠系自动化手册．中国水利水电出版社，1996
[24] 吕宏兴，裴国霞，杨玲霞．水力学[M]，中国农业出版社，2002
[25] 清华大学水力学教研室，余常昭主编．水力学(第四版)[M]，清华大学出版社，1994
[26] Wylie E B and StreeterV L Fluid Transients [M]. American :Mc-Graw-Hill International Book Company, 1978.
[27] E．B．怀利 VL．斯特里特著，瞬变流[M]，清华大学流体传动与控制教研组译，北京：水利电力出版社．1987．1 (注：[26]的译本)
[28] Chaudhry M H.Applied Hydraulic Transients [M].Canada:Van Nostrand Reinhold Comp., 1979.
[29] 杨开林．电站与泵站中的水力瞬变及调节[M]．北京：中国水利水电出版社，2000．
[30] 吴持恭．水力学[M]．高等教育出版社，1979
[31] 刘鹤年主编．流体力学．第二版．北京：中国建筑工业出版社，2004
[32] 齐鄂荣等编．水力学[M]．武汉水利电力大学出版社，2000
[33] 屠大燕主编．流体力学与流体机械．第一版．北京：中国建筑工业出版社1994
[34] 陈玉璞等．流体动力学[M]．河海大学出版社，1990
[35] 汪德爟．计算水力学理论与应用[M]．河海大学出版社，1989
[36] 王福军．计算流体动力学[M].北京清华大学出版社，2004
[37] 杨景芳．微机计算水力学[M]．大连理工大学出版社，1991
[38] 周雪漪．计算水力学[M]．北京清华大学出版社，1995
[39] 严镇军．数学物理方程[M]．中国科学技术大学出版社，1996
[40] 陈材侃．计算流体力学[M]．重庆出版社，1992
[41] Abbot, M.B., An Introduction to the Method of Characteristics[M]. American Elsevier, New York. 1966.
[42] 高双聚，杨玲霞．明渠非恒定流数值计算的边界处理新方法[J]．郑州工学院学报．1994 48-51
[43] 万晖．明渠非恒定流的特征线解法．黑龙江水专学报．2006 Vol．133,No．1：20-22
[44] 韩庆书，吴江航．计算流体力学的理论、方法及应用．北京：科学出版社，1998
[45] 曹叔尤．水力学及河流动力学基本问题研究的现状与任务[J]．四川大学学报(工程科学版)，Vol34,No．1,Jan．2002：1-5
[46] 刘培斌，耿六成，孙东坡等．河流工程问题数值模拟理论与实践[J]．黄河水利出版社，1999：18-24
[47] 魏文礼，金中青．复杂边界河道流速场的数值模拟[J]．水利学报，1994(11)：26-30
[48] 罗景．明渠非恒定流的有关特性及应用．武汉大学硕士学位论文，2004
[49] 杨开林．明渠结合有压管调水系统的水力瞬变计算[J]．水利水电技术，2002(4)：5-7
[50] 练继建,王俊，万五一等．变时步的特征线法计算复杂输水系统的水力过渡过程[J]．水利水电技术，2003(9)：12-14
[51] C. Taylor and K. Morgan, Computational techniques in transient and turbulent flow v.2 Recent advances in numerical methods in fluids, Swansea: Pineridge Press, 1981.
[52] 万五一，长距离分段低压输水系统水力特性研究：[硕士学位论文]，天津；天津大学，2001
[53] 郑邦民，赵昕，计算水动力学，武汉大学出版社，2001，103～114
[54] 何建京．明渠非均匀流糙率系数及水力特性研究．河海大学博士学位论文，2003
[55] 张志涌，徐彦琴等．MATLAB教程—基于6．x版本[M]．北京航空航天大学出版社，2001
[56] 求是科技编著．MATLAB 7．O从入门到精通[M]．人民邮电出版社，2006
[57] 苏金明，刘宏，刘波编著．MATLAB高级编程[M]．电子工业出版社，2005
[58] 张智星．MATLAB程序设计与应用[M]．清华大学出版社，2002
[59] 张韵华，奚梅成，陈效群．数值计算方法和算法[M]．北京科学出版社，2000
[60] 彭国伦．Fortran 95程序设计[M]．中国电力出版社
[61] 刘新民，蔡琼，白康生．Visual Basic 6．0程序设计[M]．北京清华大学出版社．2004
[62] 杨光宏．面向对象程序设计实用教程[M]．北京，机械工业出版社，2005
[63] 何济．Visual Basic数据库程序设计[M]．成都，电子科技大学出版社，2005
[64] 和克智．C++程序设计[M]．第二版．西安交通大学出版社，1999
[2] 张修真等，南水北调—中国可持续发展的支撑工程，中国水利水电出版社．1999．6
[3] 黄伟雄，徐颂，我国南水北调方案的对比与优化设想，佛山科学技术学院学报，2001，19(4)，50～56
[4] 梁海涛．南水北调中线工程河南段总干渠设计．防渗技术．1999．Vol．5N0．2．34-35
[5] 阎占元等，中线南水北调概况与区域发展研究，地域研究与开发1995．12
[6] 水利部长江水利委员会长江勘测规划设计院，南水北调中线工程规划(2001年修订)专题报告．2001．7
[7] 张志明，陈烈奔，张颖君．南水北调中线工程总干渠水面线研究[J]．人民长江2006 Vol．37，No．2
[8] 杨立信等编译，国外调水工程，北京：中国水利水电出版社，2003．
[9] 宋祖诏，张思俊，詹美礼，取水工程，北京：中国水利水电出版社，2002，1-3．
[10] 徐元明，国外跨流域调水工程建设与管理综述，人民长江，1997，28(3)，11-13．
[11] 沈佩君，邵东国，郭元裕，国内外跨流域调水工程建设的现状与前景，武汉水利电力大学学报，1995，28(5)，463～469
[12] 沈洪，国外调水工程纵横谈，四川水利，2000，21(5)，56～58
[13] Costantino,M.L.;Fiore, G.B.;Guadagni,G.;;Fumero,R;Montevecchi,F.M.Fluiddynamic optimization of the pumping oxygenator: CFD simulation and in vitro test. ASAIO Journal, vol 46,no.2, Mar-Apr, 2000
[14] Craig, K.;DeTraversay, C.:Bowen,B.;Essemiani,K.;Levecq,C.;Naylor, R.Hydra u-lic study and optimization of water treatment processes using numerical simulation. Water Science and Technology: Water Supply, Vol 2,No. 5-6,2002
[15] Yang,James (Vattenfall Utveckling AB ) ;Hemstrom,Bengt.CFD-a useful tool in spillway capacity determination.International Conference on Hydraulic Engineering Software, Hydrosoft,Proceedings,1998
[16] Chilton,Richard(Bechte Water Technology Ltd);Stainsby, Richard;Thompson, Susan.Design of the sewage sludge pumping systems. Journal of Hydraulic Research/De Recherches Hydrauliques, Vol 34,No.3, 1996
[17] 黄东，郑国栋，郑邦民．明渠非恒定流数值模拟[J]．工程设计CAD与智能建筑．1999(10)
[18] 林秉南，明渠不恒定流研究的现状和发展，林秉南论文选集，中国水利 水电出版社，2000，340～373
[19] 钱木金，蔡云美．解明渠非恒定流的混合网格法[J]．人民长江，1996
[20] 邓家泉．二维明渠非恒定水流BGK数值模拟[J]．水利学报，2002(4)
[21] 邓家泉．以玻尔兹曼方程建立明渠水流模型的理论基础[J]．人民珠江，2000(6)
[22] 余国安．闸门调控下的灌溉渠道非恒定流数值模拟研究．西北农林科技大学硕士学位论文，2004
[23] 美国内务部垦务局编著．庞进武、高占义等译．渠系自动化手册．中国水利水电出版社，1996
[24] 吕宏兴，裴国霞，杨玲霞．水力学[M]，中国农业出版社，2002
[25] 清华大学水力学教研室，余常昭主编．水力学(第四版)[M]，清华大学出版社，1994
[26] Wylie E B and StreeterV L Fluid Transients [M]. American :Mc-Graw-Hill International Book Company, 1978.
[27] E．B．怀利 VL．斯特里特著，瞬变流[M]，清华大学流体传动与控制教研组译，北京：水利电力出版社．1987．1 (注：[26]的译本)
[28] Chaudhry M H.Applied Hydraulic Transients [M].Canada:Van Nostrand Reinhold Comp., 1979.
[29] 杨开林．电站与泵站中的水力瞬变及调节[M]．北京：中国水利水电出版社，2000．
[30] 吴持恭．水力学[M]．高等教育出版社，1979
[31] 刘鹤年主编．流体力学．第二版．北京：中国建筑工业出版社，2004
[32] 齐鄂荣等编．水力学[M]．武汉水利电力大学出版社，2000
[33] 屠大燕主编．流体力学与流体机械．第一版．北京：中国建筑工业出版社1994
[34] 陈玉璞等．流体动力学[M]．河海大学出版社，1990
[35] 汪德爟．计算水力学理论与应用[M]．河海大学出版社，1989
[36] 王福军．计算流体动力学[M].北京清华大学出版社，2004
[37] 杨景芳．微机计算水力学[M]．大连理工大学出版社，1991
[38] 周雪漪．计算水力学[M]．北京清华大学出版社，1995
[39] 严镇军．数学物理方程[M]．中国科学技术大学出版社，1996
[40] 陈材侃．计算流体力学[M]．重庆出版社，1992
[41] Abbot, M.B., An Introduction to the Method of Characteristics[M]. American Elsevier, New York. 1966.
[42] 高双聚，杨玲霞．明渠非恒定流数值计算的边界处理新方法[J]．郑州工学院学报．1994 48-51
[43] 万晖．明渠非恒定流的特征线解法．黑龙江水专学报．2006 Vol．133,No．1：20-22
[44] 韩庆书，吴江航．计算流体力学的理论、方法及应用．北京：科学出版社，1998
[45] 曹叔尤．水力学及河流动力学基本问题研究的现状与任务[J]．四川大学学报(工程科学版)，Vol34,No．1,Jan．2002：1-5
[46] 刘培斌，耿六成，孙东坡等．河流工程问题数值模拟理论与实践[J]．黄河水利出版社，1999：18-24
[47] 魏文礼，金中青．复杂边界河道流速场的数值模拟[J]．水利学报，1994(11)：26-30
[48] 罗景．明渠非恒定流的有关特性及应用．武汉大学硕士学位论文，2004
[49] 杨开林．明渠结合有压管调水系统的水力瞬变计算[J]．水利水电技术，2002(4)：5-7
[50] 练继建,王俊，万五一等．变时步的特征线法计算复杂输水系统的水力过渡过程[J]．水利水电技术，2003(9)：12-14
[51] C. Taylor and K. Morgan, Computational techniques in transient and turbulent flow v.2 Recent advances in numerical methods in fluids, Swansea: Pineridge Press, 1981.
[52] 万五一，长距离分段低压输水系统水力特性研究：[硕士学位论文]，天津；天津大学，2001
[53] 郑邦民，赵昕，计算水动力学，武汉大学出版社，2001，103～114
[54] 何建京．明渠非均匀流糙率系数及水力特性研究．河海大学博士学位论文，2003
[55] 张志涌，徐彦琴等．MATLAB教程—基于6．x版本[M]．北京航空航天大学出版社，2001
[56] 求是科技编著．MATLAB 7．O从入门到精通[M]．人民邮电出版社，2006
[57] 苏金明，刘宏，刘波编著．MATLAB高级编程[M]．电子工业出版社，2005
[58] 张智星．MATLAB程序设计与应用[M]．清华大学出版社，2002
[59] 张韵华，奚梅成，陈效群．数值计算方法和算法[M]．北京科学出版社，2000
[60] 彭国伦．Fortran 95程序设计[M]．中国电力出版社
[61] 刘新民，蔡琼，白康生．Visual Basic 6．0程序设计[M]．北京清华大学出版社．2004
[62] 杨光宏．面向对象程序设计实用教程[M]．北京，机械工业出版社，2005
[63] 何济．Visual Basic数据库程序设计[M]．成都，电子科技大学出版社，2005
[64] 和克智．C++程序设计[M]．第二版．西安交通大学出版社，1999